Conference publications

Abstracts

XVII conference

Peculiarities of mechanics of the structured particles

Somsikov V.M.

Institute of Ionosphere, Almaty, 050020, Kazakhstan

Any fundamental theory is basing on axiomatic statements and models. It defines area of theory application. The classical mechanics is not an exception. Using abstract concepts of a material point (MP) and a hard body by means of a unique postulate it is possible to deduce all its basic equations. Such postulate is the postulate A: «work of forces of reaction is always equal to zero on any virtual moving МP which is not breaking the set of the kinematic connections» [1]. Leaning against a postulate A, under condition of potentiality of collective forces within the frames of the accepted models the Hamilton formalism is developed.

However in the real nature the МP and hard bodies do not exist. All nature bodies possess structure and all processes in nature are dissipative. It leads to difficulties at the description of nonequilibrium systems. The nature of these difficulties is caused by that processes in nonequilibrium systems are irreversible and as has proved Poincare, within the limits of a formalism of Hamilton dynamics of systems is reversible [2]. It is determined the restriction of the classical mechanics.

It was shown that the dynamics of the structured particles (SP) is irreversible and described by the equation of motion including potential and non-potential forces. Irreversibility is caused by the work of the non-potential forces which transform the motion energy of SP into internal energy [3-5]. So, if to replace МP on SP the expanded classical mechanics for description of the irreversible dynamics of nonequilibrium systems is appearing.

The purpose of the report is to show how basing on the concept of symmetry the mechanics SP consisting of potentially interacting MP is appeared. Unlike the established representations, it is entered two types of symmetry: symmetry of space-time and symmetry of system. It is shown, how from character of symmetry it is possible to obtain analytical expression of energy. It has shown that in conformity with two types of symmetry appear two types of energy: internal energy of system and energy of its motion in space.

The motion equation of SP is obtained by differentiation the expression of SP energy on time. With the help of D’Alambert equations the Lagrange, Hamilton and Liouville equations for the systems consisting from SP are obtained. The peculiarities of these equations are that the collective forces causing evolution of nonequilibrium systems taking into account. It is shown how mechanics SP leads to thermodynamics laws and as the concept of entropy is appearing in classical mechanics.

References

1. Lanczos С. The variation principles of mechanics. University of Toronto press. 1962, 408p

2. Prigogine I. From the being to becoming. М, 1980, 343p.;

3. Somsikov V.M. Equilibration of a hard-disks system// International Jour. Bifurcation and Chaos. 2004, 14, 11, p. 4027-4031;

4. Somsikov V.M. Thermodynamics and classical mechanics. Journal of Physics. 2005, 23, p.7-16;

5. Somsikov V.M.. The irreversibly mechanics of the systems of structured particles. Chaotic Modeling and Simulation International Conference Chania, Crete, Greece, June 1-5, 2009. p.1-7.

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